Beginning and Intermediate Algebra with Graphing Calculators An Integrated Approach

by Cochener, Deborah J.; Hodge, Bonnie M.; Gustafson, R. David

• ISBN13: 9780534359423
• ISBN10: 0534359426
• Format: Hardcover
• Copyright: 1999-11-05
• Publisher: Brooks Cole

Summary

The calculator is required - it is not optional. Calculator instruction is keyed to the TI-83 - TI 86. The approach throughout the text is fourfold: NUMERICAL, specifically through the use of tables; GRAPHICAL, done both on graph paper and with the graphing calculator, also providing the student with opportunities to model data and to interpret models; SYMBOLIC, which helps the student link the numerical and graphical; and finally VERBAL, where students are required to express mathematical concepts in their own words.

Table of Contents

PREFACE	ix
1 Basic Arithmetic and Graphing Calculator Concepts	1	(62)
1.1 Review of Fractions	2	(18)
Technology 1.1: Introduction to the Graphing Calculator	14	(6)
1.2 Exponents and Order of Operations	20	(9)
Technology 1.2: Using the STOre Key	27	(2)
1.3 Adding and Subtracting Real Numbers	29	(9)
1.4 Multiplying and Dividing Real Numbers	38	(7)
1.5 Basic Applications	45	(11)
Chapter Summary	56	(3)
Chapter Test	59	(2)
Careers & Mathematics	61	(2)
2 Exponents and Polynomials	63	(44)
2.1 Whole-Number Exponents	64	(7)
2.2 Algebraic Expressions and Polynomials	71	(7)
2.3 Adding and Substracting Polynomials	78	(5)
2.4 Multiplying Polynomials	83	(7)
2.5 Dividing Polynomials by Monomials	90	(3)
2.6 Dividing Polynomials by Polynomials	93	(7)
Chapter Summary	100	(2)
Chapter Test	102	(1)
Cumulative Review: Chapter 1 and 2	102	(3)
Careers & Mathematics	105	(2)
3 Modeling Linear Equations in One and Two Variables	107	(78)
3.1 Introduction to Linear Equations in One Variable	108
3.2 Literal Equations and Formulas	18
3.3 Introduction to Equations in Two Variables	123	(10)
3.4 The Rectangular Coordinate Systems	133	(24)
Technology 3.4: Graphing Basics	151	(6)
3.5 Linear Applications and Models	157	(8)
Technology 3.5: INTERSECT Method for Solving	165	(1)
3.6 Algebraic and Graphical Solutions to One-Variable Linear Equations	165	(13)
Chapter Summary	178	(3)
Chapter Test	181	(2)
Careers & Mathematics	183	(2)
4 An Extended Look at Applications and Absolute Value Equations	185	(34)
4.1 Applications--A Numeric Approach	186	(9)
4.2 Business Applications	195	(5)
4.3 More Applications of Equations	200	(5)
4.4 Equations Containing Absolute Value	205	(6)
Chapter Summary	211	(2)
Chapter Test	213	(1)
Cumulative Review: Chapters 3 and 4	214	(3)
Careers & Mathematics	217	(2)
5 Factoring	219	(44)
5.1 Using the Distributive Property to Factor	220	(8)
5.2 Factoring Trinomials	228	(8)
5.3 Factoring the Difference of Two Squares and a Summary of Factoring Techniques	236	(8)
5.4 Using Factoring to Solve Equations	244	(13)
Chapter Summary	257	(3)
Chapter Test	260	(1)
Careers & Mathematics	261	(2)
6 Rational Expressions and Equations	263	(53)
6.1 Simplifying Rational Expressions	264	(8)
6.2 Adding and Subtracting Rational Expressions	272	(7)
6.3 Multiplying and Dividing Rational Expressions	279	(4)
6.4 Mixed Operations and Complex Fractions	283	(6)
6.5 Algebraic and Graphical Solutions of Rational Equations	289	(11)
6.6 Applications of Rational Equations	300	(6)
Chapter Summary	306	(4)
Chapter Test	310	(1)
Cumulative Review: Chapters 5 and 6	311	(3)
Careers & Mathematics	314	(2)
7 Making the Transition from Elementary to Intermediate Algebra	316	(78)
7.1 Negative Integral Exponents	317	(9)
7.2 Review of Factoring	326	(5)
7.3 Equation Review	331	(11)
7.4 Graphing and Its Applications Revisited	342	(15)
Technology 7.4: ROOT/ZERO Method for Solving	356	(1)
7.5 Solving Simple Linear Inequalities	357	(11)
7.6 Compound Inequalities	368	(10)
7.7 Absolute Value Inequalities	378	(7)
Chapter Summary	385	(5)
Chapter Test	390	(2)
Careers & Mathematics	392	(2)
8 Functions	394	(56)
8.1 Relations and Functions	395	(11)
8.2 Functions and Graphs	406	(5)
8.3 Slope of a Nonvertical Line	411	(10)
8.4 Equations of Lines	421	(9)
8.5 Variation	430	(9)
Chapter Summary	439	(5)
Chapter Test	444	(1)
Cumulative Review: Chapters 7 and 8	444	(4)
Careers & Mathematics	448	(2)
9 Rational Exponents and Radicals	450	(53)
9.1 Introduction to Roots and Radicals	451	(6)
9.2 Rational Exponents and Simplifying Radical Expressions	457	(8)
9.3 Arithmetic Operations with Radicals	465	(7)
9.4 Radical Equations and Their Applications	472	(9)
9.5 Radical Functions	481	(7)
9.6 (XXX)-1 and Complex Numbers	488	(9)
Chapter Summary	497	(3)
Chapter Test	500	(1)
Careers & Mathematics	501	(2)
10 Quadratics	503	(58)
10.1 Square Root Property and Completing the Square	504	(9)
10.2 The Quadratic Formula and the Discriminant	513	(9)
10.3 Applications of Quadratic Functions and Solutions of Equations Using Quadratic Methods	522	(9)
10.4 Graphs of Quadratic Functions	531	(9)
10.5 Quadratic and Other Inequalities	540	(11)
Chapter Summary	551	(3)
Chapter Test	554	(1)
Cumulative Review: Chapter 9 and 10	555	(4)
Careers & Mathematics	559	(2)
11 Functions and Their Inverses	561	(60)
11.1 Algebra of Functions	562	(7)
11.2 Inverse Functions	569	(9)
11.3 Exponential Functions	578	(11)
11.4 Logarithmic Functions	589	(9)
11.5 Properties of Logarithms	598	(8)
11.6 Exponential and Logarithmic Equations	606	(7)
Chapter Summary	613	(4)
Chapter Test	617	(2)
Careers & Mathematics	619	(2)
12 Systems of Equations and Inequalities	621
12.1 Solving Systems of Two Equations in Two Variables	622	(8)
12.2 Applications of Systems of Two Equations in Two Variables	630	(9)
12.3 Solving Systems of Three Equations in Three Variables	639	(6)
12.4 Using Matrices to Solve Systems of Equations	645	(9)
12.5 Using Determinants to Solve Systems of Equations	654	(7)
12.6 Systems of Inequalities	661	(6)
Chapter Summary	667	(2)
Chapter Test	669	(1)
Cumulative Review: Chapter 11 and 12	670	(3)
Careers & Mathematics	673
APPENDIX A CONIC SECTIONS	A-1	(13)
APPENDIX B BINOMIAL THEOREM	A-14	(5)
APPENDIX C ARITHMETIC AND GEOMETRIC SEQUENCES	A-19	(9)
APPENDIX D PERMUTATIONS AND COMBINATIONS	A-28	(8)
APPENDIX E ANSWERS TO SELECTED EXERCISES	A-36
GLOSSARY/INDEX	I-1	(5)
APPLICATIONS INDEX	I-6